On the uniqueness of meromorphic functions that share small functions on annuli

Da Wei Meng; San Yang Liu; Nan Lu; Da Wei Meng; San Yang Liu; Nan Lu

doi:10.3934/math.2020207

AIMS Mathematics

2020, Volume 5, Issue 4: 3223-3230. doi: 10.3934/math.2020207

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Research article

On the uniqueness of meromorphic functions that share small functions on annuli

School of mathematics and statistics, Xidian University, Xi’an, Shanxi, 710126, P. R. China

Received: 31 December 2019 Accepted: 17 March 2020 Published: 27 March 2020
MSC : 30D30, 30D35

In this paper, we aim to investigate the uniqueness of meromorphic functions that share small functions on annuli. As a matter of fact, we give several uniqueness theorems about meromorphic functions sharing four or three distinct small functions on the annulus $\mathbb{A} = \{z:\frac{1}{R_{0}} < |z|< R_{0}\},$ where 1 < $R_{0}\leq+\infty.$ To some extent, our theorems extend the previous work by T. B. Cao, H. X. Yi and H. Y. Xu, and also generalize the work by N. Wu and Q. Ge.
- uniqueness,
- meromorphic functions,
- transcendental,
- annuli,
- sharing small functions
Citation: Da Wei Meng, San Yang Liu, Nan Lu. On the uniqueness of meromorphic functions that share small functions on annuli[J]. AIMS Mathematics, 2020, 5(4): 3223-3230. doi: 10.3934/math.2020207

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Abstract

In this paper, we aim to investigate the uniqueness of meromorphic functions that share small functions on annuli. As a matter of fact, we give several uniqueness theorems about meromorphic functions sharing four or three distinct small functions on the annulus $\mathbb{A} = \{z:\frac{1}{R_{0}} < |z|< R_{0}\},$ where 1 < $R_{0}\leq+\infty.$ To some extent, our theorems extend the previous work by T. B. Cao, H. X. Yi and H. Y. Xu, and also generalize the work by N. Wu and Q. Ge.

References

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